A253046 An involution of the natural numbers: if n = 2*p_i then replace n with 3*p_{i+1}, and conversely if n = 3*p_i then replace n with 2*p_{i-1}, where p_i denotes the i-th prime.
1, 2, 3, 9, 5, 15, 7, 8, 4, 21, 11, 12, 13, 33, 6, 16, 17, 18, 19, 20, 10, 39, 23, 24, 25, 51, 27, 28, 29, 30, 31, 32, 14, 57, 35, 36, 37, 69, 22, 40, 41, 42, 43, 44, 45, 87, 47, 48, 49, 50, 26, 52, 53, 54, 55, 56, 34, 93, 59, 60, 61, 111, 63, 64, 65, 66, 67
Offset: 1
Keywords
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- A. B. Frizell, Certain non-enumerable sets of infinite permutations. Bull. Amer. Math. Soc. 21 (1915), no. 10, 495-499.
- Index entries for sequences that are permutations of the natural numbers
Programs
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Haskell
a253046 n | i == 0 || p > 3 = n | p == 2 = 3 * a000040 (i + 1) | otherwise = 2 * a000040 (i - 1) where i = a049084 (div n p); p = a020639 n -- Reinhard Zumkeller, Dec 26 2014 -
Mathematica
a253046[n_] := Block[{f}, f[x_] := Which[PrimeQ[x/2], 3 NextPrime[x/2], PrimeQ[x/3], 2 NextPrime[x/3, -1], True, x];Array[f, n]]; a253046[67] (* Michael De Vlieger, Dec 27 2014 *) -
Python
from sympy import isprime, nextprime, prevprime def A253046(n): q2, r2 = divmod(n,2) if not r2 and isprime(q2): return 3*nextprime(q2) else: q3, r3 = divmod(n,3) if not r3 and isprime(q3): return 2*prevprime(q3) return n # Chai Wah Wu, Dec 27 2014
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